Exact symbolic verification code for Complex slices, inverses, and deformations of a three-dimensional real algebra
Description
Supplementary Python code for the manuscript "Complex slices, inverses, and deformations of a three-dimensional real algebra". The program reconstructs the defining multiplication table and performs 185 exact symbolic checks of algebraic identities, multiplication operators, inverse formulas, singular cases, symmetry constraints, and trace invariants for the parameter family. The package includes the verification program, dependency specification, execution instructions, and a guide linking the checks to the manuscript’s results. It requires Python 3 and SymPy 1.14.0. All calculations use exact arithmetic. The computations complement the mathematical proofs presented in the manuscript.
Files
Steps to reproduce
1. Download and extract `supplementary_material.zip`. 2. Using Python 3.13, open a terminal in the extracted folder. 3. Install the dependency: `python3 -m pip install -r requirements.txt` 4. Run the verification program: `python3 verify_certificates.py` 5. Successful execution prints: `PASS: 185 exact symbolic checks (SymPy 1.14.0).` No external input files are required. All computations use exact symbolic arithmetic. A failed check raises an exception identifying the check and its residual.